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Q: find extreme Value of function fex, y) = x°t 3xy?-3x²-3y=t7 1

A: Given:  fx,y=x3+3xy2-3x2-3y2+7 ⇒fx=3x2+3y2-6x, fy=6xy-6y To find extreme points put fy=0, fx=0…

Q: Vy - y 3 b) dy 2 y²

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Q: Consider the points A(2, a,0), B(0,1,B),C(1,1,B) where aand Bare negative real numbers. Find a and…

A: To add or subtract, two or more vectors add or subtract the corresponding components of each vector.

Q: Pow thal lel; and onlr

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Q: Solue! A Sx+ x-y) dx + x dy =0

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Q: Evaluate (x² + y²) dxdy

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Q: 2. For F = (xz3, 2y*x²,5z?y) find: a. div F b. Curl F and find div(curl F) C.

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Q: Let C z-1=3 and1 = §, = dz. Then

A: The solution is given as

Q: 2x + 2y + z = 16 x + z = 34 y − 3z = 34

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Q: /| r? dr dy ; N: 1 + y < 4r, I< 2, y 2 0

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Q: Reverse the order of integration and evaluate the double integral dxdy

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Q: If * x=t -1, y = +t, find y"

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Q: O campute dyldx and X= 4t3-t² + 7t Y= t4 - lot

A: As we know that the chain rule: dydx=dydt×dtdx The Power law: ddxxn=nxn-1 The Quotient rule:…

Q: 3. (x +2 ) Ex²-4)

A: y=(x+2)3x2-4

Q: 2x Eyaluate dx . 1-4x4

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Q: Vxdx 2. For J T-Vx use 4 O u = JA u = x O u = Ja

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Q: a2z If z = In(x² + y²), find a²z + dx2 ду?

A: Given, z=lnx2+y2

Q: Find V · (V x F), if F(x, y, z) = 5e*?i+ 9xe"j – 6e²k. V · (V × F) =

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Q: Evalude x Lucx+4) dx

A: Given that a integration and we solve it by using general formulas of integration. Here i attached…

Q: Evaluate F. dr along the line segment C from Pto Q. F = -8 xi+5y j; P(-1,0), Q(7, 0) F. dr i

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Q: Q5: Evaluate f(secx)³ dx

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Q: Exc. Eind. Lim (x-1) y3

A: Solution:

Q: Q. / 3sec3xtan3xdx sec3x +c -sec3x +c O None O tan3x +oс

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Q: cln5 18) Simplify S e 2x-3dx In2

A: To Determine: Simplify the given integral

Q: Find dz if 4x2 + 9y-z z²= 5e

A: The given equation is: 4xz+9y-z3=5ez...(1)

Q: ex Find FaイNR f6つき,2)→1-2XY+x4

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Q: =wyx for w = In (3x+ 4y). ух

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Q: where u=24 x+86. Then A

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Q: he side, and y values are across the ple to evaluate f(4, 2).

A: The table for f(x,y) we evaluate f(4,2)

Q: y = x² + x y = x + 5 2

A: y=x2+x y=x+5   a2-b2=(a-b)(a+b)